Template for a cone?

[Goldie]

SWMBO is doing a canvaswork job for a friend and needs to construct a truncated cone in canvas. Unfortunately, the boat is miles away so she's having to rely on measurements supplied which are:

Cone base circumference: 156cm

Diameter of the truncated end: 4cm

Slant distance from the base to the truncated top: 48cm

It may be easier to construct the cone whole and to forget about the truncation - just modifying it in situ, in which case the slant measurement would obviously be increased. Do you good folk have any suggestions as to the easiest way to calculate and draw the template in 2D - i.e. onto the canvas please? SWMBO will work out seam allowances etc when the template is drawn.

Many thanks in anticipation -after all, I can't see many of us sailing today

 

[sarabande]

sorry. Mathematical nonsense. earlybird is right.

Bbrain not engaged with fingers. Been up nearly all night with tree problems.

 

[earlybird]

if the circumference is 156, then the diameter is 156/pi = 49.6 cm
So, on a piece of newspaper
1 at the bottom of the page, draw a horizontal line 49.6 cm long
.

Can't agree, that would give a cone of base circumference of 49.6 cm. not 156 cm as required.
My calc. gives a pattern size of a 170 deg. sector of a circle of 106 cm dia. ie not quite a semi-circle. For the truncation, a sector of 10 cm dia. is removed. All sizes approximate.
any other offers ?
Thinks:- Must now find something useful to do!!!

 

[VicS]

Well I make it 171° of a circle radius 52.2 cm (104.4cm diam) with a circle radius 4.2 cm cut out.
But maybe my maths is a bit rusty.

 

[earlybird]

Well I make it 171° of a circle radius 52.2 cm (104.4cm diam) with a circle radius 4.2 cm cut out.
But maybe my maths is a bit rusty.

No, it's probably just because your GPS is set to a different datum

 

[Goldie]

Sincere thanks from both SWMBO and myself to all 3 of you.

Sarabande; I hope you get a good nights sleep and your trees are still where they should be!

VicS and Earlybird, particular thanks to you guys for the number crunching and VicS, I even understood the working! I'll be template making tomorrow.

Best Regards, Ian.

 

[cliff]

Base circ = 156cm => base Ø= 156/pi = 49.656 cm

x/4=(48+x)/49.656 => x=4*((48+x))/49.656 => x=4.205 => total slant height = (48+4.205) =>52.2cm

arc°=(360*156)/(2*pi*52.2) => 171.228°

Pattern => r1=52.2cm, r2=4.2cm, arc°=171.228°

(VicS's maths is NOT as rusty as mine (got to lay off the "Aqua Vita")

 

[VicS]

(VicS's maths is a little rusty)

Oh no!

You have this wrong: x/4=48/49.656

x is the length of the sloping sides of the small triangle (base length 4cm)

The length of the sloping sides of the large triangle (base 49.66cm) is (48+x) not 48.


so that should be x/4 = (48+x)/49.656


(Have to confess to making the same mistake at first)

 

[Shiver Metimbers]

Trial and error, newspaper is very cheap, just draw and cut till you get it right. If you want the Engineering answer then you will find all you need here, good luck.

http://mathworld.wolfram.com/Cone.html

 

[srp]

Trial and error....

There's no need to guess though. Any sheet metal worker or traditional draughtsman will tell you that the development of a cone is just a segment of a circle. Vic and Cliff show the maths to enable you to calculate it, and a sheet metal worker would draw it out with a pair of compasses.
Comparing the accuracy of the mathematical vs the practical methods, Vic and Cliff show the answer accurate to 3 decimal points, whereas a sheet metal worker would get it absolutely spot on.....

 

[Goldie]

And just in case anybody's interested..... I can confirm that SWMBO now has a perfectly fitting pair of cones Calculations proved spot on (to 3 decimal places). Thanks again to one and all.

 

[Shiver Metimbers]

There's no need to guess though. Any sheet metal worker or traditional draughtsman will tell you that the development of a cone is just a segment of a circle. Vic and Cliff show the maths to enable you to calculate it, and a sheet metal worker would draw it out with a pair of compasses.
Comparing the accuracy of the mathematical vs the practical methods, Vic and Cliff show the answer accurate to 3 decimal points, whereas a sheet metal worker would get it absolutely spot on.....

What about the bit for the join, you cannot weld or fold join canvas, at least with my idea they would have realised they would need a hem for the joint before they cut their canvas.

I also give them a link to all the clever mathimatical stuff.

 

[alahol2]

And just in case anybody's interested..... I can confirm that SWMBO now has a perfectly fitting pair of cones Calculations proved spot on (to 3 decimal places). Thanks again to one and all.

A pair? Her name's not Madonna is it?

 

[VicS]

What about the bit for the join, you cannot weld or fold join canvas, at least with my idea they would have realised they would need a hem for the joint before they cut their canvas

Go to the original post and RTFQ then you will find "SWMBO will work out seam allowances etc when the template is drawn."


Goldie
Tnx for letting us know it all worked., but what are they for?


.

 

[Goldie]

Goldie Tnx for letting us know it all worked., but what are they for? .

A friend has bought himself a RIB (as a safety boat for his sailing sons) and it came with a protective cover which only extended as far as the transom. To keep the UVs off the PVC (the boat is stored on a trailer outside) he wanted some protective covers for the pointy bits to as far forward as the transom. SWMBO makes our canvaswork anyway, and is too much of a perfectionist to just sew up some big condoms so she wanted to make fitted covers. Delivered today and they fit the bill perfectly. A couple of black bin liners would have done, but wouldn't have looked half as smart! Thanks again for you help.

 

[LadyInBed]

truncated cone in canvas.(

Given all these precise calculations, has any margin been allowed for canvas shrinkage